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Damping of zero sound in Luttinger liquids

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  • P. Pirooznia
  • P. Kopietz

Abstract

We calculate the damping γ q of collective density oscillations (zero sound) in a one-dimensional Fermi gas with dimensionless forward scattering interaction F and quadratic energy dispersion k 2 / 2 m at zero temperature. Using standard many-body perturbation theory, we obtain γ q from the expansion of the inverse irreducible polarization to first order in the effective screened (RPA) interaction. For wave-vectors | q| /k F ≪F (where k F =m v F is the Fermi wave-vector) we find to leading order γ q ∝| q | 3 /(v F m 2 ). On the other hand, for F ≪| q| /k F most of the spectral weight is carried by the particle-hole continuum, which is distributed over a frequency interval of the order of q 2 /m. We also show that zero sound damping leads to a finite maximum proportional to |k - k F | -2 + 2 η of the charge peak in the single-particle spectral function, where η is the anomalous dimension. Our prediction agrees with photoemission data for the blue bronze K 0.3 MoO 3 . We comment on other recent calculations of γ q . Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Suggested Citation

  • P. Pirooznia & P. Kopietz, 2007. "Damping of zero sound in Luttinger liquids," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 58(3), pages 291-296, August.
    • Handle: RePEc:spr:eurphb:v:58:y:2007:i:3:p:291-296
    DOI: 10.1140/epjb/e2007-00235-y
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